相关论文: An optimization problem for triangles

We consider the problem of minimizing a convex function over the intersection of finitely many simple sets which are easy to project onto. This is an important problem arising in various domains such as machine learning. The main difficulty…

We consider the problem of finding an optimal piecewise linear path (polygonal line) connecting two given points with the possibility of making n turns at some points (the absolute value of each turn angle does not exceed a prescribed…

We address an optimal reachability problem for a planar manipulator in a constrained environment. After introducing the optmization problem in full generality, we practically embed the geometry of the workspace in the problem, by…

In this paper the problem of maximizing the distance to a given fixed point over an intersection of balls is considered. It is known that this problem is NP complete in the general case, since any subset sum problem can be solved upon…

We consider a long-term optimal investment problem where an investor tries to minimize the probability of falling below a target growth rate. From a mathematical viewpoint, this is a large deviation control problem. This problem will be…

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise…

The orienteering problem is a route optimization problem which consists in finding a simple cycle that maximizes the total collected profit subject to a maximum distance limitation. In the last few decades, the occurrence of this problem in…

Optimization problems have been the subject of statistical physics approximations. A specially relevant and general scenario is provided by optimization methods considering tradeoffs between cost and efficiency, where optimal solutions…

We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…

In a multiobjective optimization problem a solution is called Pareto-optimal if no criterion can be improved without deteriorating at least one of the other criteria. Computing the set of all Pareto-optimal solutions is a common task in…

In this research paper, the problem of optimization of a quadratic form over the convex hull generated by the corners of hypercube is attempted and solved. It is reasoned that under some conditions, the optimum occurs at the corners of…

By first solving the equation $x^3+y^3+z^3=k$ with fixed $k$ for $z$ and then considering the distance to the nearest integer function of the result, we turn the sum of three cubes problem into an optimisation one. We then apply three…

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…

This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…

We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…

We consider the problem of minimising the number of edges that are contained in triangles, among $n$-vertex graphs with a given number of edges. We prove a conjecture of F\"uredi and Maleki that gives an exact formula for this minimum, for…

In this paper, we consider optimization problems w.r.t. to pairs of orthogonal matrices $XY = I$. Problems of this form arise in several applications such as finding shape correspondence in computer graphics. We show that the space of such…

We consider a project that consists of a set of activities performed in parallel under constraints on their start and finish times, including start-finish precedence relationships, release start times, release end times, and deadlines. The…

The multi-objective optimization is to optimize several objective functions over a common feasible set. Since the objectives usually do not share a common optimizer, people often consider (weakly) Pareto points. This paper studies…

In this paper we consider resource allocation problem stated as a convex minimization problem with linear constraints. To solve this problem, we use gradient and accelerated gradient descent applied to the dual problem and prove the…